Methods of in-vitro analysis using time-domain NMR spectroscopy

ABSTRACT

An in vitro method of determining an analyte concentration of a sample includes placing the sample into a low-field, bench-top time-domain nuclear magnetic resonance (TD-NMR) spectrometer. The NMR spectrometer is tuned to measure a selected type of atom. A magnetic field is applied to the sample using a fixed, permanent magnet. At least one 90 degree radio-frequency pulse is applied to the sample. The radio-frequency pulse is generally perpendicular to the magnetic field. The 90 degree radio-frequency pulse is removed from the sample so as to produce a decaying NMR signal. The decaying NMR signal is measured at a plurality of times while applying a plurality of 180 degree refocusing radio-frequency pulses to the sample. The analyte concentration is calculated from the plurality of measurements associated with the decaying NMR signal and a selected model.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.11/794,920, filed on Jul. 9, 2007, which is a U.S. national stage ofInternational Application No. PCT/US2006/001327, filed on Jan. 13, 2006,which claims the benefit of U.S. Provisional Application No. 60/643,896,filed on Jan. 14, 2005, each of which is hereby incorporated byreference herein in its entirety.

FIELD OF THE INVENTION

The present invention relates generally to methods of determining ananalyte concentration of a sample. More particularly, the presentinvention relates to methods of determining an analyte using alow-field, time-domain nuclear magnetic resonance (NMR) spectrometer.

BACKGROUND OF THE INVENTION

The quantitative determination of analytes in body fluids is of greatimportance in the diagnoses and maintenance of certain physiologicalabnormalities. Some non-limiting examples of analytes that may bemonitored in certain individuals include cholesterol (e.g., HDL, LDL,total), triglycerides, globulin, albumin, total protein, blood ureanitrogen, creatinine, and alkaline phosphastase.

Nuclear magnetic resonance (NMR) spectroscopy is an analytical anddiagnostic technique that is used for structural and quantitativeanalysis of one or more analytes in a sample. One specific type of NMRis time domain nuclear magnetic resonance (TD-NMR). TD-NMR spectrometersare used for spin-lattice (T₁) and spin-spin (T₂) relaxationmeasurements. NMR spectrometers have been used to analyze body fluidsamples, such as blood plasma. NMR is based on nuclear magneticproperties of certain elements and isotopes of those elements. One suchelement that is commonly analyzed by NMR is hydrogen, which has a singleproton and an intrinsic nuclear spin. Hydrogen is present in manyanalytes of interest and has high natural abundance. When hydrogennuclei are placed in a magnetic field, they adopt one of two allowedorientations. Therefore, the resulting magnetic moment can be alignedwith the magnetic field or opposed to the magnetic field. The twoorientations are separated by an amount of energy that depends on thestrength of the magnetic field and the strength of the interactionbetween the hydrogen nucleus and the field. The energy difference may bedetermined by applying an electromagnetic pulse at a characteristicresonance frequency, which causes the nuclei aligned with the field(lower energy state) to align against the field (higher energy state).

The resonance frequency, ν, of a hydrogen nucleus is dependent on thestrength of the magnetic field, Bo, and is given by:ν=γB _(o)/2πwhere ν is in units of MHz, B_(o) is in units of tesla (T) and γ is thefundamental gyromagnetic ratio for hydrogen (¹H) and is equal to267.512×10⁶ rad T⁻¹s⁻¹. Magnetic field strengths commonly used for NMRspectroscopy are in the range of from 1.4 to 14.1 T, corresponding tohydrogen resonance frequencies of from 60 to 600 MHz. Since hydrogen isthe most common nucleus studied, NMR spectrometers are often classifiedby their hydrogen resonance frequencies instead of their actual magneticfield strengths.

The two most common types of magnets used in NMR spectrometers arepermanent magnets and superconducting magnets. Although permanentmagnets provide acceptable field stability and are less costly, thefield strength is limited to approximately 1.4 T (60 MHz).

In contrast, superconducting magnets can provide much higher fields inthe range of from about 4.7 to about 18.8 T (from 200 to 800 MHz). It isimportant to remember that the resonance frequencies of hydrogen nuclei,as well as other non-identical nuclei, are proportional to the fieldstrength. Neighboring nuclei, in the same molecule or in the solvent,may greatly impact the resonance frequency of a particular hydrogennucleus. Therefore, to obtain characteristic NMR spectra with highresolution, it is desirable to use the higher magnetic fields achievedwith superconducting magnets. Unfortunately, NMR systems that utilizesuperconducting magnets are very expensive, require cryogenic coolingwith liquid nitrogen and liquid helium, and are very large (commonlyoccupying an entire room). In addition to field strength, the stabilityand homogeneity of the magnetic field should be controlled to obtainhigh-quality NMR spectra. High-field NMR spectrometers also employspecial locking electronics to compensate for small field instabilities.In the sample probe, additional electronic hardware is used to controlthe homogeneity of the magnetic field by a process called shimming.

Additionally, the resulting high-resolution NMR spectra are complex andmust be interpreted by a highly-trained scientist. The individuals whooperate the high-resolution NMR equipment need to be well-trained.High-resolution NMR spectroscopy typically involves acquiring a completespectrum and identifying peaks for qualitative and quantitativeanalysis.

Therefore, it would be desirable to provide a method of determining theconcentration of one or more analytes using NMR that provides lowercosts and is a convenient method to use without requiring highly-trainedoperators or scientists.

SUMMARY OF THE INVENTION

According to one method, an analyte concentration of a sample isdetermined in vitro by placing the sample into a low-field, bench-toptime-domain nuclear magnetic resonance (TD-NMR) spectrometer. The NMRspectrometer is tuned to measure a selected type of atom. A magneticfield is applied to the sample using a fixed, permanent magnet. At leastone 90 degree radio-frequency pulse is applied to the sample. The 90degree radio-frequency pulse is generally perpendicular to the magneticfield. The 90 degree radio-frequency pulse is removed from the sample soas to produce a decaying NMR signal. The decaying NMR signal is measuredat a plurality of times while applying a plurality of 180 degreerefocusing radio-frequency pulses to the sample. The analyteconcentration is calculated from the plurality of measurementsassociated with the decaying NMR signal and a selected model.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a front view of an NMR spectrometer according to oneembodiment.

FIG. 2 is a flowchart of determining an analyte concentration accordingto one method.

DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENT

The present invention is directed to a method of using a time-domainnuclear magnetic resonance (TD-NMR) spectrometer to determine theanalyte concentration of a sample. The method is done in vitro and maybe performed without using reagents. The term, in vitro, is definedherein as being an artificial environment outside the living organism(e.g., a petri dish or test tube). The present invention is anticipatedto be used in hospitals and clinics, but it is contemplated that it maybe used in other locations.

Some non-limiting examples of analytes that may be monitored in certainindividuals include glucose, cholesterol (e.g., HDL, LDL, total),triglycerides, globulin, albumin, total protein, blood urea nitrogen,alkaline phosphastase, and creatinine. The present invention is notlimited, however, to these specific analytes. The analytes may be in,for example, body fluid such as a blood serum sample, a blood plasmasample or a urine sample.

The spectrometer is a low-field, TD-NMR spectrometer. The term“low-field” as defined herein is a magnetic field being generally lessthan 1.4 T (tesla). TD-NMR spectrometers employ at least one fixed,permanent magnet, and hydrogen resonance frequencies of 10, 20 and 60MHz are common. According to one embodiment, the TD-NMR spectrometerincludes a magnetic field less than 1.4 T and does not include shimmingor locking electronics or hardware.

TD-NMR spectrometers used in the present invention measure spin-spin(T₂) relaxation. Information about analytes is obtained directly fromthe T₂ relaxation signals or portions thereof. The TD-NMR spectrometeris a bench-top instrument, which means that the spectrometer may beoperated while positioned on or to a bench. The bench-top TD-NMRspectrometer may be of different sizes.

The TD-NMR spectrometer is tuned to measure a selected type of atom. Forexample, it is contemplated that the TD-NMR spectrometer may be used tomeasure atoms such as hydrogen, fluoride, and phosphorous. It isdesirable, however, for the TD-NMR spectrometer to be tuned to measurehydrogen because of its abundance.

The TD-NMR spectrometer includes a fixed permanent magnet and does notrequire the use of reagents. It is contemplated that an NMR contrastagent may be added to the sample to enhance the detection of theselected analyte. It is contemplated that the TD-NMR spectrometer,however, may include more than one fixed, permanent magnet.

Referring to FIG. 1, a spectrometer 10 is shown according to oneembodiment. The spectrometer 10 includes a first permanent magnetic 12,a second permanent magnetic 14, an RF transmitter 16, a receiver 18, apulse generator 20, a computer 22 and an RF coil 24. The first andsecond permanent magnets 14,16 provide a magnetic field. The pulsegenerator 20 triggers the RF transmitter 14, which outputsradio-frequency pulses to the RF coil 24 and eventually to a sample 26in a sample tube 28. The receiver 18 receives and converts the decayingNMR signals to a digitized form. The computer 22 uses the digitizedsignals from the receiver to calculate the analyte concentration.

One example of a TD-NMR spectrometer that may be used is a 20 MHzbench-top Bruker Minispec NMR spectrometer. The Bruker Minispec TD-NMRspectrometer has a 10 mm probe and a fixed 0.47 tesla magnet stabilizedat 40° C. To control homogeneity, the temperature of the magnet may beprecisely controlled such as to the nearest one-thousandth of a degree.The present invention, however, is not limited to this particular TD-NMRspectrometer. It is contemplated that other TD-NMR spectrometers may beused in the methods of the present invention.

According to the present invention, an analyte concentration of a sampleis determined using an TD-NMR spectrometer and is performed in vitro.The analyte concentration of the sample may be determined in the absenceof reagents. Information about analytes is obtained directly from the T₂relaxation signals or portions thereof.

Referring to FIG. 2, an in vitro method of determining an analyteconcentration of a sample comprises the step 102 of placing a sampleinto an NMR spectrometer. In step 104, a magnetic field is applied tothe sample. In step 106, at least one 90 degree radio-frequency (RF)pulse is applied to the sample. In step 108, the 90 degreeradio-frequency pulse is removed from the sample so as to produce adecaying NMR signal. In step 110, the decaying NMR signal is measured ata plurality of times while applying a plurality of 180 degree refocusingradio-frequency pulses to the sample. In step 112, the analyteconcentration is calculated from the plurality of measurementsassociated with the decaying NMR signal and a selected model.

According to another method, a sample is placed into a low-field,time-domain nuclear magnetic resonance (TD-NMR) spectrometer. Forexample, the sample may be placed into the TD-NMR spectrometer byplacing a few milliliters of sample into a 10-mm diameter sample tube,which is then inserted into the spectrometer probe. The tube istypically a generally round shape, but it is contemplated that the tubemay be of other shapes.

One example of a sample size that may be used is two milliliters of ablood serum sample, a blood plasma sample or other body fluids such asurine. It is contemplated that the TD-NMR spectrometer may be designedto have different sample sizes, which may result in an underfill oroverfill condition relative to the coil. Using, for example, a BrukerMinispec TD-NMR spectrometer, a sample size of two milliliters (orgreater) results in an overfill condition. In an overfill condition, thesampled volume is determined by the coil geometry. Therefore, the T₂relaxation measurements of multiple samples analyzed in two or moremilliliter quantities may be relatively compared and used forcalibration. However, if quantities less than two milliliters are used,the sample volume does not completely fill the coil, which results in anunder fill condition. Since the resulting T₂ relaxation profile willdepend upon the absolute amount of sample in the coil, it is necessaryto weigh each sample before analysis with the TD-NMR spectrometer. Theresulting T₂ signal for each sample is divided by the weight of thatsample. The adjusted T₂ measurements may then be used for comparison andcalibration. When working with small sample volumes in an under fillsituation, it is desirable to have at least enough sample to produce anNMR signal that is at least three times greater than the noise of themeasurement.

The NMR spectrometer is tuned to measure at least one selected type ofatom. The at least one selected type of atom may include hydrogen,fluoride, or phosphorous.

A first magnetic field is applied to the sample using a fixed, permanentmagnet. The term “fixed” refers to the spacing being constant betweenthe magnet and the sample, and the term “permanent” means that anintrinsic naturally-occurring magnetic field is associated with themagnet. Before the first magnetic field is applied, the nuclear magneticmoments of each proton (e.g., a hydrogen proton) are randomly oriented.After the first magnetic field is applied, a number of the nuclearmagnetic moments of the protons orient themselves with the field, whilea smaller number orient themselves against the first magnetic field. Anet magnetization for the sample develops since the number of nuclearmagnetic moments in each direction is not equal.

At least one radio-frequency (RF) pulse is applied to the sample todetect the sample's net magnetization. The radio-frequency pulse isgenerally perpendicular (i.e., about 90 degrees) to the first magneticfield and creates a second magnetic field. This radio-frequency pulsemay be referred to as an excitation RF pulse. One method foraccomplishing this radio-frequency pulse is by applying an alternatingvoltage across the ends of an NMR probe that induces an alternatingmagnetic field throughout the sample. Because the second magnetic fieldcreated by the RF pulse rotates the nuclear magnetic moments that hadbeen oriented with or against the first magnetic field, the netmagnetization of the sample is then no longer oriented in the samedirection as the first magnetic field. After the individual magneticmoments are oriented by applying the RF pulse, they precess about theaxis of the second magnetic field at a frequency that is dependent onthe field strength. The precession of these spins generates a smalloscillating magnetic field that is detected as an alternating current ina detection coil.

The RF pulse is removed from the sample so as to produce a decaying NMRsignal. This causes the selected protons to return to their equilibriumcondition through various relaxation processes. The precession frequencyof each proton is dependent on the local field strength. Since the fieldof the first magnetic field is not uniform, sample protons canexperience different field strengths. As each proton is in a differentmagnetic field due to its nearest neighbors, each magnetic momentprecesses at a slightly different frequency. This difference inprecession frequencies causes the precession of the individual momentsto de-phase. To compensate for the loss of phase coherence due toinhomogeneity in the first magnetic field, a plurality of 180 degreerefocusing RF pulses is applied to the sample in order to measure thedecaying NMR signal. The rate of decay is characterized by the spin-spinrelaxation time, T₂. The sequence of the RF pulses applied to the samplefollows the Carr-Purcell pulse sequence.

Relaxation produces a decaying NMR signal that is characteristic of thesample. The shape of the overall signal is the convolution of the decaysrepresenting all unique proton environments in the sample. The decayingNMR signal is measured at a plurality of times. The analyteconcentration is calculated directly from the plurality of measurementsof the decaying NMR signal.

To determine the concentration of an analyte in a sample, the NMRspectrometer is calibrated. Specifically, the analyte concentration in asample is determined by applying a selected calibration model for theparticular analyte to the plurality of signals associated with thedecaying NMR relaxation signal. It is contemplated that several modelsmay be used to calibrate the NMR spectrometer. One such example of acalibration method is described below.

According to one method, a selected calibration model for a specificanalyte may be developed by first measuring the NMR relaxation for aplurality of samples, known as the calibration set. The measurements areperformed of the range of the interest for the desired analyte. Theanalyte concentration in these samples may also be determinedindependently by a second reference method. One selected model that maybe used a multivariate calibration model that uses for examplechemometric techniques.

Chemometric techniques, such as, but not limited, to partial leastsquares (PLS) or principal components regression (PCR) may be used todevelop a predictive model for the analyte of interest using the samplesbelonging to the calibration set. In such an analysis, the plurality ofpoints comprising the relaxation for each sample is used as the X-matrixand the reference analyte concentrations for each sample comprise theY-matrix.

The plurality of NMR signals comprising the NMR relaxation may be useddirectly or preprocessed in a number of ways. According to one method,all of the plurality of NMR signals are used without any processing.According to another method, a subset of the plurality of NMR signalsare used without any processing.

The signal may be modified by applying techniques wherein the pluralityof measurements includes data that is representative of the originalmeasurements after preprocessing for smoothing. The plurality ofmeasurements may include a subset of the data that is representative ofthe original measurements after preprocessing for smoothing. One exampleof a smoothing technique is Savitsky-Golay smoothing.

The signal may be fitted to various polynomials, such as, but notlimited to, a exponential functional fit or a biexponential functionalfit In such cases, the X-matrix uses the transformed NMR relaxation.Alternatively, only a subset of the plurality of the original ortransformed NMR signals may be selected for analysis. A number ofchemometric procedures to be used for selecting subsets are known tothose skilled in the art.

A mulivariate calibration model using a chemometric technique such asPLS is developed using the samples of the calibration set through aprocess known as cross-validation. A portion of the samples comprisingthe calibration set, known as the training set, is used to develop amodel for the analyte of interest. Models with an increasing number ofPLS factors are constructed to predict the analyte reference values(Y-matrix) using the NMR relaxation data, processed or otherwise(X-block).

The calibration models are validated using the remaining members of thecalibration set referred to as the test set. The calibration models, asspecified by a set of regression components for a specific number of PLSfactors, are applied to the NMR relaxation data for the samples in thetest set. The error between the predicted analyte value (x pred) and thereference value (x ref) for each sample in the test set may becalculated for each calibration model. To assess the quality of thecalibration model, it is customary to use a statistic such as thestandard error of cross validation (SECV) given bySECV=[Σ(x _(pred) −x _(ref))/n−k) ]^(1/2)

-   -   where n=number of samples in the test set;    -   and k=number of PLS factors in the model.

The calibration process may be repeated an iterative number of timeswith different members of the calibration set assigned to either thetraining or test set.

The optimum model is one that minimizes the prediction error for thesamples of the test set, but contains a minimum number of PLS factors.Statistical tests may be applied to determine whether the improvement inthe prediction error with an increase in the number of PLS factors isstatistically significant.

After the proper number of PLS factors is determined through the crossvalidation process, a final calibration model is developed using theentire sample set of calibration samples.

The calibration model, consisting of a set of regression coefficients,may be applied to the plurality of the NMR signals comprising therelaxation of a new sample to predict the analyte concentration ofinterest.

Alternative Process A

An in vitro method of determining an analyte concentration of a sample,the method comprising the acts of:

placing the sample into a low-field, bench-top time-domain nuclearmagnetic resonance (TD-NMR) spectrometer, the NMR spectrometer beingtuned to measure a selected type of atom;

applying a magnetic field to the sample using a fixed, permanent magnet;

applying at least one 90 degree radio-frequency pulse to the sample, theradio-frequency pulse being generally perpendicular to the magneticfield;

removing the 90 degree radio-frequency pulse from the sample so as toproduce a decaying NMR signal;

measuring the decaying NMR signal at a plurality of times while applyinga plurality of 180 degree refocusing radio-frequency pulses to thesample; and

calculating the analyte concentration from the plurality of measurementsassociated with the decaying NMR signal and a selected model.

Alternative Process B

The method of process A wherein the sample is a body fluid.

Alternative Process C

The method of process B wherein the sample is a blood plasma sample.

Alternative Process D

The method of process B wherein the sample is a blood serum sample.

Alternative Process E

The method of process B wherein the sample is a urine sample.

Alternative Process F

The method of process A wherein the analyte is selected from the groupconsisting of glucose, cholesterol, triglycerides, albumin, blood ureanitrogen, alkaline phosphastase, and creatinine.

Alternative Process G

The method of process A wherein the method is a reagentless method.

Alternative Process H

The method of process A wherein the method includes adding an NMRcontrast agent to the sample to enhance the detection of the selectedanalyte.

Alternative Process I

The method of process A wherein the selected type of atom is hydrogen,fluoride, or phosphorous.

Alternative Process J

The method of process I wherein the selected type of atom is hydrogen.

Alternative Process K

The method of process A wherein the NMR spectrometer includes apermanent magnet less than about 1.4 tesla in the absence of hardware orelectronics for locking or shimming.

Alternative Process L

The method of process A wherein the selected model is a multivariatecalibration model.

Alternative Process M

The method of process L wherein the multivariate calibration model usesa chemometric technique.

Alternative Process N

The method of process M wherein the chemometric technique uses partialleast squares (PLS).

Alternative Process O

The method of process M wherein the chemometric technique uses principalcomponents regression (PCR).

Alternative Process P

The method of process A wherein the plurality of measurements is all ofthe measurements in the absence of processing.

Alternative Process Q The method of process A wherein the plurality ofmeasurements is a subset of all of the measurements in the absence ofprocessing.

Alternative Process R

The method of process A wherein the plurality of measurements includesdata that is representative of the original measurements afterpreprocessing for smoothing.

Alternative Process S

The method of process A wherein the plurality of measurements includes asubset of data that is representative of the original measurements afterpreprocessing for smoothing.

Alternative Process T

The method of process A wherein the plurality of measurements includesdata that is representative of the original measurements afterpreprocessing by fitting to a function.

Alternative Process U

The method of process T wherein the original measurements arepreprocessed using an exponential functional fit.

Alternative Process V

The method of process T wherein the original measurements arepreprocessed using a biexponential functional fit.

Alternative Process W

The method of process T wherein the plurality of measurements includes asubset of data that is representative of the original measurements afterpreprocessing by fitting to a function.

Alternative Process X

The method of process W wherein the original measurements arepreprocessed using an exponential functional fit.

Alternative Process Y

The method of process W wherein the original measurements arepreprocessed using a biexponential functional fit.

While the invention is susceptible to various modifications andalternative forms, specific methods thereof have been shown by way ofexample in the drawings and will herein be described in detail. Itshould be understood, however, that it is not intended to limit theinvention to the particular methods disclosed but, on the contrary, theintention is to cover all modifications, equivalents, and alternativesfalling within the spirit and scope of the invention as defined by theappended claims.

1. An in vitro method of determining an analyte concentration of asample, the method comprising the acts of: adding an NMR contrast agentto the sample to enhance detection of the analyte; placing the sampleinto a low-field, bench-top time-domain nuclear magnetic resonance(TD-NMR) spectrometer, the NMR spectrometer being tuned to measure aselected type of atom; applying a magnetic field to the sample; applyingat least one radio-frequency pulse to the sample; removing theradio-frequency pulse from the sample so as to produce a decaying NMRsignal; measuring the decaying NMR signal; and calculating the analyteconcentration from the measurement associated with the decaying NMRsignal and a selected model.
 2. The method of claim 1, wherein thesample is a body fluid.
 3. The method of claim 2, wherein the sample isa blood plasma sample.
 4. The method of claim 2, wherein the sample is ablood serum sample.
 5. The method of claim 2, wherein the sample is aurine sample.
 6. The method of claim 1, wherein the method is areagentless method.
 7. The method of claim 1, wherein the model is amultivariate calibration model.
 8. The method of claim 1, wherein theNMR spectrometer includes a permanent magnet less than about 1.4 teslain the absence of hardware or electronics for locking or shimming.
 9. Anin vitro method of determining an analyte concentration of a sample, themethod comprising the acts of: placing the sample into a low-field,bench-top time-domain nuclear magnetic resonance (TD-NMR) spectrometer,the NMR spectrometer being tuned to measure a selected type of atom;applying a magnetic field to the sample; applying at least oneradio-frequency pulse to the sample; removing the radio-frequency pulsefrom the sample so as to produce a decaying NMR signal; measuring thedecaying NMR signal; and calculating the analyte concentration from themeasurement associated with the decaying NMR signal and a multivariatecalibration model.
 10. The method of claim 9, wherein the multivariatecalibration model uses a chemometric technique.
 11. The method of claim10, wherein the chemometric technique uses partial least squares (PLS).12. The method of claim 10, wherein the chemometric technique usesprincipal components regression (PCR).
 13. The method of claim 10,further comprising fitting the decaying NMR signal to a polynomialfunction.
 14. A method of determining an analyte concentration of asample, the method comprising the acts of: developing a multivariatecalibration model by measuring NMR relaxation for a plurality ofcalibration samples; measuring a NMR relaxation for a sample with anuclear magnetic resonance (NMR) spectrometer; comparing the measurementof the sample to the multivariate calibration model to identify thedifferences between the calibration model and the measurement of thetest sample; and calculating the analyte concentration from thecomparison of the sample to the multivariate calibration model.
 15. Themethod of claim 14, wherein the multivariate calibration model uses achemometric technique.
 16. The method of claim 15 wherein thechemometric technique uses at least one of partial least squares (PLS)and principal components regression (PCR).
 17. The method of claim 15,wherein developing the multivariate model comprises: selecting a set oftraining samples from the calibration samples; developing a first modelfor the analyte with NMR relaxation measurements for the trainingsamples; selecting a set of test samples from the calibration samplesnot selected for the set of training samples; and validating the firstmodel by comparing NMR relaxation measurements of test samples to valuespredicted by the first model.
 18. The method of claim 17, furthercomprising: selecting a second set of training samples from thecalibration samples; developing a second model for the analyte with NMRrelaxation measurements for the training samples of the second set oftraining samples; selecting a second set of test samples from thecalibration samples not selected for the second set of training samples;and validating the second model by comparing NMR relaxation measurementsof test samples of the second set of test samples to values predicted bythe second model.
 19. The method of claim 18, further comprising:comparing the validation of the first model to the validation of thesecond model using a statistical test; identifying a number of partialleast squares (PLS) factors; and developing a final calibration modelusing the NMR relaxation measurements for all of the calibrationsamples.
 20. The method of claim 14, wherein the NMR spectrometer is alow-field, bench-top time-domain nuclear magnetic resonance (TD-NMR)spectrometer.